A researcher is investigating variables that might be associated with the academic performance of high school students.She examined data from 1990 for each of the 50 states plus Washington,DC.The data included information on the following variables. As part of her investigation,she ran the multiple regression model SATM = $\beta$₀ + $\beta$₁($ per pupil)+ $\beta$₂(% taking)+ $\varepsilon$_i, Where the deviations $\varepsilon$_i were assumed to be independent and Normally distributed with a mean of 0 and a standard deviation of $\sigma$.This model was fit to the data using the method of least squares.The following results were obtained from statistical software. Suppose we wish to test the hypotheses H₀: $\beta$₁ = $\beta$₂ = 0 versus H_a: at least one of the $\beta$_j is not 0,using the ANOVA F test.What is the value of the F statistic? A)3.32 B)24.0 C)79.65 D)159.3

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The ANOVA F test compares the variation explained by the regression model (the sum of squares of the regression, SSR) to the variation that is not explained by the model (the sum of squares of the residuals, SSE). The F statistic is computed as F = (SSR/p) / (SSE/(n-p-1)), where p is the number of independent variables in the model, and n is the sample size. From the ANOVA table, we have SSR = 1898.96, SSE = 2667.23, p = 3, and n = 51. Substituting these values into the formula, we get F = (1898.96/3) / (2667.23/47) = 79.65. The p-value for this F statistic is less than 0.001, indicating strong evidence against the null hypothesis H₀, and in favor of the alternative hypothesis H_a. Therefore, we conclude that at least one of the coefficients F1F1F1S1F1F1F10_j is not zero, and that the model is a good fit for the data.

A Researcher Is Investigating Variables That Might Be Associated with the Academic